演算法

A numerical calculation program is written up for the various solution methods in this paper and the program is being used in various aspects of inverse problem of environmental hydraulics, including inverse problem in reverse process of one-dimensional unstable diffusion, inverse problem in reverse process of convection-diffusion, inverse problem for the dispersion coefficient in water quality model, The inverse problem of coefficient identification for nonlinear Boussinesq equation, parameter identification inverse problem for water quality model, the inversion of parameter of BOD-DO water model, the inverse problem of the source of convection-diffusion, identification of the steady-state permeability for two dimensional isotropic medium, two-dimensional steady inverse problem of convection-diffusion and parameter identification inverse problem for two-dimensional parabolic equation, etc.

对本文提出的各种算法，编制了数值计算程序，并把它应用于环境水力学反问题诸多领域，包括污染物一维非恒定扩散逆过程反问题，对流扩散方程逆过程反问题，河流水质纵向弥散系数反问题，非线性Boussinesq方程反问题，河流水质多参数识别反问题，BOD-DO水质模型参数反演问题，对流—扩散方程源项反问题及二维恒定各向同性介质渗透系数反问题，二维定常对流——扩散方程及二维抛物型方程参数控制反问题等。

The least square conjugate gradient and odd values decomposition method also can be used to perform tomographic inversion.

研制的最小平方共轭梯度算法和奇异值分解法也可进行同样的层析反演。

Regarding to this inverse problem, it is solved by the conjugate gradient method for the stable solution and quick convergence.

在反演求解时，使用共轭梯度算法，以保证求解的稳定性，加快解的收敛速度。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

Electromagnetic fields, caused by high frequency loop current on layer earth, are computed numerically by direct integral of Gauss quadrature, continued fraction expansion and Padé approximation using Matlab language.

在层状介质情况下，本文提出采用直接积分方法——高斯改进型积分、连分式展开法，对高频谐变回线电流产生的电磁场进行正演计算，采用MATLAB语言实现算法。

We apply a differential evolution algorithm to study parameter inversion of two-dimensional wave equation.

利用微分进化算法进行二维波动方程参数反演的研究。

Key words two-dimensional wave equation; parameter inversion; differential evolution algorithm; finite element

利用微分进化算法进行二维波动方程参数反演的研究。

This is done by working the Euclidean algorithm backward.

反演Euclidean算法即可，相除得到的商非常重要。

Based analysis above, we chose the spatial resolution of 1°×1°in the horizontal direction and 5~30 km in depth. Using the pseudobending method to calculate the ray traveling path and residual of travel time; LSQR method to inverse, we got the final 3-D P wave velocity structure in this area.

根据上述分析，以水平方向1°×1°，垂直方向以5 km、15 km、30 km为间隔划分网格，并建立初始速度模型，采用伪弯曲射线追踪方法计算走时和射线路径，通过基于LSQR算法的反演重建了研究区域40 km以下、480 km以上的三维P波速度结构。

Based on the spherical harmonic functions expansion and finite difference for discretization of transport equation, an inverse power scheme is presented for calculation of the k-eigenvalue problem.

基于球谐函数展开和有限差分离散，给出了中子输运方程的源项反演逼近的反幂算法，该方法的优势是在适当的初值条件下可以显著提高计算速度。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。